Let f:with input D produces output Real numbers. Let x 1 be an accumulation point of D. Then f has a limit (L) at x 1 if and only if for every sequence {x n } converging to x 1 with x n in D, (x n not...

Let f:with input D produces output Real numbers. Let x₁
be an accumulation point of D.  Then f has a limit (L) at x₁
if and only if for every sequence {x_n} converging to x₁
with x_n
in D, (x_n
not equal to x₁) for all n, the sequence {f(x_n)} converges.  I understand that this is a way to prove a limit of a function, that this uses sequences to prove a limit of a function.

Your help is appreciated . Please be complete in your explanations.  Thank you.